1. \( 2 \frac{3}{4}+1 \frac{2}{3}= \) *Must show work*

First, let's convert the mixed numbers into improper fractions. For \( 2 \frac{3}{4} \), we calculate: \[ 2 \times 4 + 3 = 8 + 3 = 11 \] So, \( 2 \frac{3}{4} = \frac{11}{4} \). For \( 1 \frac{2}{3} \), we calculate: \[ 1 \times 3 + 2 = 3 + 2 = 5 \] So, \( 1 \frac{2}{3} = \frac{5}{3} \). Now we add the two improper fractions: \[ \frac{11}{4} + \frac{5}{3} \] To do this, we need a common denominator. The least common multiple of \( 4 \) and \( 3 \) is \( 12 \). Now we convert each fraction: \[ \frac{11}{4} = \frac{11 \times 3}{4 \times 3} = \frac{33}{12} \] \[ \frac{5}{3} = \frac{5 \times 4}{3 \times 4} = \frac{20}{12} \] Now we can add them: \[ \frac{33}{12} + \frac{20}{12} = \frac{53}{12} \] Finally, we convert \( \frac{53}{12} \) back to a mixed number: \[ 53 \div 12 = 4 \text{ remainder } 5 \] So, \( \frac{53}{12} = 4 \frac{5}{12} \). Thus, \( 2 \frac{3}{4}+1 \frac{2}{3} = 4 \frac{5}{12} \).